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Pertanyaan

Diketahui panjang vektor p ​ dan q ​ berturut-turut adalah . Besar sudut antara vektor adalah 6 0 ∘ . Tentukan panjang vektor ( p ​ − q ​ ) .

Diketahui panjang vektor  berturut-turut adalah begin mathsize 14px style 7 space dan space 15 end style. Besar sudut antara vektor begin mathsize 14px style straight p with rightwards arrow on top space dan space straight q with rightwards arrow on top end style adalah . Tentukan panjang vektor .

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panjang vektor adalah 13.

panjang vektor begin mathsize 14px style open parentheses straight p with rightwards arrow on top minus straight q with rightwards arrow on top close parentheses end style adalah 13.

Pembahasan

Berdasarkan informasi di atas, maka didapatkan: Jadi, panjang vektor adalah 13.

Berdasarkan informasi di atas, maka didapatkan:

vertical line straight p with rightwards arrow on top minus straight q with rightwards arrow on top vertical line equals square root of vertical line straight p with rightwards arrow on top vertical line squared plus space vertical line straight q with rightwards arrow on top vertical line squared minus 2 vertical line straight p with rightwards arrow on top vertical line vertical line straight q with rightwards arrow on top vertical line cos space straight alpha end root vertical line straight p with rightwards arrow on top minus straight q with rightwards arrow on top vertical line equals square root of 7 squared plus 15 squared minus left parenthesis 2 times 7 times 15 times cos space 60 degree right parenthesis end root vertical line straight p with rightwards arrow on top minus straight q with rightwards arrow on top vertical line equals square root of 49 plus 225 minus 210 times left parenthesis 1 half right parenthesis end root vertical line straight p with rightwards arrow on top minus straight q with rightwards arrow on top vertical line equals square root of 169 vertical line straight p with rightwards arrow on top minus straight q with rightwards arrow on top vertical line equals 13

Jadi, panjang vektor begin mathsize 14px style open parentheses straight p with rightwards arrow on top minus straight q with rightwards arrow on top close parentheses end style adalah 13.

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